# Conjugacy test using Solvable radical method.
gap> p:=Group((14,27,40,53,66,79,92,105,118,131,144,157)(15,28,41,54,67,80,
>     93,106,119,132,145,158)(16,29,42,55,68,81,94,107,120,133,
>     146,159)(17,30,43,56,69,82,95,108,121,134,147,160)(18,31,44,
>     57,70,83,96,109,122,135,148,161)(19,32,45,58,71,84,97,110,
>     123,136,149,162)(20,33,46,59,72,85,98,111,124,137,150,
>     163)(21,34,47,60,73,86,99,112,125,138,151,164)(22,35,48,61,
>     74,87,100,113,126,139,152,165)(23,36,49,62,75,88,101,114,
>     127,140,153,166)(24,37,50,63,76,89,102,115,128,141,154,
>     167)(25,38,51,64,77,90,103,116,129,142,155,168)(26,39,52,65,
>     78,91,104,117,130,143,156,169),
>   (2,92,21)(3,105,35)(4,118,49)(5,131,63)(6,144,77)(7,157,91)(8,
>     14,93)(9,27,107)(10,40,121)(11,53,135)(12,66,149)(13,79,
>     163)(15,106,22)(16,145,38)(17,54,44)(18,41,56)(19,119,
>     75)(20,80,85)(23,67,123)(24,158,143)(25,28,146)(26,132,
>     167)(29,120,36)(30,159,52)(31,68,58)(32,55,70)(33,133,
>     89)(34,94,99)(37,81,137)(39,42,160)(43,134,50)(45,82,72)(46,
>     69,84)(47,147,103)(48,108,113)(51,95,151)(57,148,64)(59,96,
>     86)(60,83,98)(61,161,117)(62,122,127)(65,109,165)(71,162,
>     78)(73,110,100)(74,97,112)(76,136,141)(87,124,114)(88,111,
>     126)(90,150,155)(101,138,128)(102,125,140)(104,164,169)(115,
>     152,142)(116,139,154)(129,166,156)(130,153,168));;
gap> a:=(2,71,89,130,101,35,131,55,108,20,44,168,151)(3,85,103,132,115,
> 49,144,69,122,34,58,26,165)(4,99,117,146,129,63,157,83,136,48,
> 72,28,23)(5,113,119,160,143,77,14,97,150,62,86,42,37)(6,127,133,
> 18,145,91,27,111,164,76,100,56,51)(7,141,147,32,159,93,40,125,
> 22,90,114,70,65)(8,155,161,46,17,107,53,139,36,104,128,84,67)(9,
> 169,19,60,31,121,66,153,50,106,142,98,81)(10,15,33,74,45,135,79,
> 167,64,120,156,112,95)(11,29,47,88,59,149,92,25,78,134,158,126,
> 109)(12,43,61,102,73,163,105,39,80,148,16,140,123)(13,57,75,116,
> 87,21,118,41,94,162,30,154,137);;
gap> b:=(2,147,169,51,14,110,59,140,34,94,128,83,74)(3,161,15,65,27,124,
> 73,154,48,108,142,97,88)(4,19,29,67,40,138,87,168,62,122,156,
> 111,102)(5,33,43,81,53,152,101,26,76,136,158,125,116)(6,47,57,
> 95,66,166,115,28,90,150,16,139,130)(7,61,71,109,79,24,129,42,
> 104,164,30,153,132)(8,75,85,123,92,38,143,56,106,22,44,167,
> 146)(9,89,99,137,105,52,145,70,120,36,58,25,160)(10,103,113,151,
> 118,54,159,84,134,50,72,39,18)(11,117,127,165,131,68,17,98,148,
> 64,86,41,32)(12,119,141,23,144,82,31,112,162,78,100,55,46)(13,
> 133,155,37,157,96,45,126,20,80,114,69,60);;
gap> erg:=TFCanonicalClassRepresentative(Group(GeneratorsOfGroup(p)),[a,b]);;
gap> a^(erg[1][4]/erg[2][4])=b;
true
